Worked example finding the radius, period, and frequency of the circular motion of an electron in a uniform magnetic field.

Showing the circular motion of electrons in the magnetic field of a Helmholtz coil using a gas-filled glass tube.

Definition, including the Lorentz force on a charge moving in a magnetic field. Definition of Tesla and Gauss units for the strength of a magnetic field.

Explanation of how electrons are used to make image in a TV screen, with a demonstration showing that a magnet will distort this picture when placed near the screen.

Finding the force on a moving charge in an electric and magnetic field. Finding the total force on a wire in a magnetic field.

Circular motion of moving particles in constant magnetic fields. Finding the radius of the circular path, with an example for an electron moving in a 1T magnetic field.

Using an electron gun and a magnet to show that the path of an electron will curve in the presence of a magnetic field.

Definition, with examples of use in separating uranium isotopes for the atomic bomb and for separating isotopes for medical radiation treatments.

Definition, with explanation of how a cyclotron is used to accelerate particles with an electric field while containing the particles with a magnetic field. Mention of the use of rings as modern particle accelerators.

Pictures and discussion of an early cyclotron as well as two modern examples of particle accelerators: Fermilab and CERN.

Definition, with images of their use in making visible the tracks of electrons and other charged particles. Discussion of the discovery of positrons and other new particles.

Tracking the motion of electrons and alpha particles in a cloud chamber.

Introduction to magnetism with example of bar magnet. Magnetic field of a bar magnet with diagram; Bar magnets are dipoles. Magnetic monopoles do not exist in isolation. Magnetic Gauss's Law that magnetic flux through a closed surface is zero. Earth's magnetic field, with diagrams and link to a visualization of a bar magnet and Earth's magnetic field

Moving charges in a magnetic field feel force perpendicular to both velocity v of charge and direction of magnetic field B. Cross products and the right hand rule, with diagrams and link to a visualization. Lorentz Force F = q(E + v x B), with example of a velocity selector.

Using pressure and tension from E and B fields to understand forces felt by charges. Includes links to visualizations.

Force and torque on a rectangular current loop in a uniform magnetic field. Magnetic dipole moment μ is defined, with links to visualizations of how torque tends to align μ with B. Force on a magnetic dipole in a non-uniform field, with diagrams. Links to visualizations showing the force on one dipole from another dipole.

Electric potential; Lorentz force and magnetic force; Biot-Savart Law; Magnetic dipole moments

Table of important values and equations for resistors, capacitors, and inductors. Brief review of what happens in RC, RL, LC, and RLC circuits.

Magnetic dipoles and their fields are defined, as well as the Lorentz force on a moving charge in a magnetic field.

Definition of the magnetic dipole moment, with diagrams and equations for force and torque on a magnetic dipole.

Magnetism from empirical evidence; Lorentz force on charges and wires; electron trajectories; applications to modern physics; work done by B-fields.

B-fields defined; force on moving charge, straight wire; F = 0 for current loop.

Circular and helical motion of charges in B-field; velocity selector and mass spectrometry.

Using vector product; worked problems on rolling and suspended conducting rods, moving charges, and bar magnet.

Three questions about forces on moving charges in magnetic fields, with answers and explanations.

Question about the sign of charge carriers in a slab in a magnetic field, with answer and explanation.

Question about force on one moving charge from another, with answer and explanation.

Question about the attraction between free dipoles, with answer and explanation.

Question about force and torque on a magnetic dipole in a Helmholtz Coil, with answer and explanation.

Describing motion of a particle in parallel E and B fields.

Solution (PDF)^#

Can a resting electron be set in motion with a constant B-field?

Solution (PDF)^#

Describing trajectory of an ion through E-field, then B-field.

Solution (PDF)^#

Finding momentum of nucleus in the Large Hadron Collider and corresponding B-field or E-field.

Solution (PDF)

Determining the mass of a particle given its radius of motion in a magnetic field.

Solution (PDF)

Force on electron; balancing electric and magnetic forces.

Solution (PDF)

4-part problem; finding E-field, trajectories for particle; computing kinetic energy. Solution not included.

Finding relative charges given trajectories for three particles.

Solution (PDF)

Video animation showing the magnetic field of the earth as well as the magnetic field of the solar wind, which carries the magnetic field of the sun out to the neighborhood of the earth.

Video animation demonstrating the process of magnetic merging, which is the cause of solar flares.

Applet showing the interaction between the magnetic field lines of the earth and a bar magnet in a classroom at MIT.

Video animation of the magnetic field created by a moving positive charge.

Video animation of the magnetic field created by a moving negative charge.

Video animation showing the magnetic field created by a charge moving in a circular path.

Video animation showing the magnetic field generated by two charges moving in a circular path.

Video animation showing the magnetic field generated by four charges moving in a circular path.

Video animation showing the magnetic field generated by eight charges moving in a circular path.

Video animation showing the magnetic field and force on a charge moving out of the page in a magnetic field that is uniform but changing in strength.

Video animation showing the motion of a charge moving through a uniform upward magnetic field.

Video animation showing a back view of the motion of a charge moving through a uniform upward magnetic field.

Video animation showing the magnetic field and behavior of a magnet suspended by a spring above a current-carrying wire loop.

Video showing a magnetic dipole moving to align with the magnetic field of the Earth, at a latitude similar to that of Boston.

Video animation showing a giant magnetic dipole moving to align with Earth's magnetic field.

Video animation showing a closer view of a giant magnetic dipole moving to align with Earth's magnetic field.

Video animation showing the magnetic field and motion of a magnet between two coils with sinusoidal and out of phase current.

Video animation showing the magnetic field of a magnet suspended between two coils with currents that are sinusoidal and in phase.

Video animations showing the force felt by a charge moving into and then out of a uniform magnetic field.

Applet simulating the magnetic field of a magnetic dipole which is rotating in a uniform magnetic field.

Interactive applet simulating the behavior of a magnet attached to a spring between two coils with varying currents.